Schema for vertical declining dials

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A dial constructed using Waugh's schema Waughs vertical decliner method (1973)-(full).svg
A dial constructed using Waugh's schema

Vertical declining dials are sundials that indicate local apparent time. Vertical south dials are a special case: as are vertical north, vertical east and vertical west dials. The word declining means that the wall is offset from one of these 4 cardinal points. There are dials that are not vertical, and these are called reclining dials. [1]

Contents

A sundial schema uses a compass and a straight edge to firstly derive the essential angles for that latitude, then to use this to draw the hourlines on the dial plate. In modern terminology this would mean that graphical techniques were used to derive and and from it . [lower-alpha 1]

Basic calculation

There are four basic angles that are needed to construct a vertical declining dial, Waugh described them such: [2]

The four basic calculation have a certain symmetry.

Waugh's method 1973

Finding SD- the substyle length
Finding SH - the substyle height
Drawing the hourlines

At this point only three lines matter, the vertical, the substyle length and substyle height. A circle marked off in 15° angles is needed (circular protractor).

Wigham-Richardson's method

Before the protractor became ubiquitous, compasses and the Scale of Chords were used for laying out an angle. This method originally used them.

Finding SD
Finding SH and the centre of the equinoctial
Drawing the hourlines

At this point only three lines matter, the vertical, the substyle length and substyle height. A circle marked off in 15° angles is needed (circular protractor).

Use of Dialing rulers

Foster Serles Dialling Scales (1638) Foster is credited for producing a set of scales to assist in the laying out of the hour line on a dial. To use them SH and SD must already be known. The scales are placed on the SD line, and lines are drawn using the calculated SH value rather than the actual latitude.

Zarbula method

Zarbula is credited with the design of over a hundred sundials in Hautes Alpes and Piedmont. This region straddles the 45 ° parallel and as such his dials are a special case. He worked directly on the wall, and didn't require to know the latitude or the declination of the dial, these we found by observation. His dials were examples of frescos, and all gave five-minute accuracy.

Laying out the dial

All the rest of the dial was laid out using a 45° square, with a 15° measure at the end. [lower-alpha 7]

See also

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References

Footnotes
  1. The British Sundial Society publishes a glossary of computer terms and the symbols that are commonly used to represent them. Latitude is represented by phi, or φ or Φ.
  2. This is in degrees- divide by 15 to convert to hours.
  3. Waugh in his description is far more mathematically rigorous.
  4. Declination of the sun ( δ ) not declination of the wall (d)
  5. Indian or Hindu Circle for Sub-style determination
  6. In dialling language substyle is used like sub aqua, meaning- under the style- not like subsection, meaning a smaller part. Similarly, equation means an adjustment and height can mean a perpendicular angle.
  7. Zarbula was working within 2° of the 45th parallel, so it worked. Further north or south the triangle would need to use the latitude and co-latitude and a protractor would have been needed
  8. A combination of a 30°/ 60° square, and 45° square could also be used.
Notes
  1. Waugh 1973, Chapter 11.
  2. Waugh 1973, pp. 78–79.
  3. Waugh 1973, pp. 76–78.
  4. Wigham-Richardson, J (1900). "APPENDIX ON THE CONSTRUCTION OF SUN-DIALS". In Gatty, Margaret Scott (Mrs Alfred) (ed.). The Book of Sun-dials (4th ed.). London: George Bell & Sons. pp. 487–499.
  5. "L'Equerre et l'Oiseau".
  6. Paul Gagnaire. "L'Équerre et l'Oiseau, l'Art et la Manière de Zarbula".

Bibliography